Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x-3y &= 6 \\ 2x-3y &= -6\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-3y = -2x-6$ Divide both sides by $-3$ to isolate $y$ $y = {\dfrac{2}{3}x + 2}$ Substitute this expression for $y$ in the first equation. $-6x-3({\dfrac{2}{3}x + 2}) = 6$ $-6x - 2x - 6 = 6$ Simplify by combining terms, then solve for $x$ $-8x - 6 = 6$ $-8x = 12$ $x = -\dfrac{3}{2}$ Substitute $-\dfrac{3}{2}$ for $x$ back into the top equation. $-6( -\dfrac{3}{2})-3y = 6$ $9-3y = 6$ $-3y = -3$ $y = 1$ The solution is $\enspace x = -\dfrac{3}{2}, \enspace y = 1$.